1. Field of the Invention
The present invention generally relates to photolithography and more particularly to an improved mask and mask design methodology.
2. Description of the Related Art
Photolithography is the technology of reproducing patterns using light. As presently used in semiconductor industry, a mask pattern for a desired circuit is transferred to a wafer through light exposure, development, etch, resist strip, etc. As the feature size on a circuit becomes smaller and smaller, the circuit shape on the wafer differs from the original mask pattern more and more. In particular, corner rounding, line end foreshortening, etc. are typically observed. These phenomena are called optical proximity effects.
One of the main reasons for optical proximity effects is light diffraction. Optical proximity effects coming from light diffraction can be overcome partly if one has the choice of using a shorter wavelength source of light, with a projection system possessing a larger numerical aperture. In practice, the wavelength of an optical light source is typically fixed (e.g., 365 nm, 248 nm, 193 nm, 157 nm etc.) and there is a practical upper limit on numerical aperture. Thus, other resolution enhancement methods, including the use of phase-shifting masks and masks with serifs, have been developed to correct optical proximity effects.
The light illumination in lithography is typically a partial coherent light illumination. The aerial image for partial coherent light illumination is given by the Hopkins equation, ##EQU1##
which is a nonlinear integral involving the mask transmission function M, the coherent point-spread function (i.e., the kernel function) K, and mutual intensity function J. It is often assumed that the imaging system is translation invariant, i.e., that K(r,r)=K(r-r). In addition, a common assumption is that the mutual intensity function satisfies J(r.sub.1, r.sub.2)=J(r.sub.1 -r.sub.2). For circular or annular aperture, the point-spread function between two points depends on their distance only, K(r-r)=K(.vertline.r-r.vertline.). Under these conditions, the Hopkins equation is usually simplified to ##EQU2##
for aerial image calculations.
Two methods have been previously suggested for finding the best/suitable mask shapes under partial coherent light illumination. Y. Liu et al. "Binary and phase-shifting mask design for optical lithography," IEEE Trans. Semiconductor Manufacturing 5, 138-152 (1992), incorporated herein by reference, treats a mask as a bitmap pattern, which consists of many pixels. The amplitude transmission at each pixel could be either 1 (with a possible fixed phase) or 0. The difficulty in this approach is that there are really too many combinations--it is 2 pixels. Y.C. Pati et al., "Phase-shifting masks for microlithography: automated design and mask requirements," J. Opt. Soc. Am. A 11, 2438-2452 (1994), incorporated herein by reference, uses a method called "optimal coherent approximation," which expresses the aerial image for a partial coherent light illumination as a sum of many coherent light illuminations. If this approximation is a good one, then perfect correction to both corner rounding and line end shortening can be achieved using a method disclosed previously in U.S. patent application Ser. No. 09/167,948,now U.S. Pat. No. 6,214,494, incorporated herein by reference, which is valid exactly for either coherent or incoherent light illuminations. The real situation for a partial coherent light illumination, however, is not this simple in general.